An approach to solving parameter-dependent LMI conditions based on finite number of LMI conditions

Many researches for linear parameter varying systems focus on the approach using a parameter-dependent Lyapunov function. Analysis and controller design for linear parameter varying systems are characterized by parameter-dependent linear matrix inequalities (LMIs). We propose an approach to solving parameter-dependent LMI conditions based on a finite number of LMI conditions. The proposed method does not require any particular assumptions on the parameter dependence except continuity. We consider a class of linear parameter varying systems and apply the proposed technique to analysis of their L² gain. Finally we demonstrate its efficacy by a numerical case study